Sinx - sin2x = sin 3 х (кубически) решите.

Sinx - sin2x=sin³x

sinx-2sinxcosx=sin³x

sinx-2sinxcosx-sin³x=0

sinx (1-2cosx-sin²x) = 0

a) sinx=0, x=kπ, k∈Z

b) 1-2cosx-sin²x=0

1-2cosx - (1-cos²x) = 0

1-2cosx-1+cos²x=0

cos²x-2cosx=0

cosx (cosx-2) = 0

cosx=0, x=π/2+kπ, k∈Z

cosx-2=0, cosx=2, x∈∅

Bmecte: x=kπ/2, k∈Z